Electron (e−) and positron (e+) bunch characteristics were directly measured for the first time by using wideband beam monitors (WBMs) and a detection system at the e+ source of the SuperKEKB B-factory. Secondarily generated e− and e+ bunches after the e+-production target were identified in their dynamical capture process at locations of the WBMs under a two-bunch acceleration scheme. The longitudinal and transverse bunch characteristics, the time intervals between the e− and e+ bunches, the bunch lengths, transverse bunch positions, and bunch charges were simultaneously separately measured for each bunch as functions of the capture phase to investigate their dynamical capture process. The results show that quite symmetric behaviors of the e− and e+ bunch characteristics were observed. The new WBMs open up a new window for direct measurements of both e− and e+ bunches during their dynamical capture process and in the optimization procedure of the e+ bunch intensity in multidimensional parameter spaces at any e+ sources.

High-intensity e+ sources are indispensable and challenging in high-energy e+e colliders to achieve the high luminosity required for high-energy physics experiments. A number of excellent reviews of high-intensity e+ sources1,2 in high-energy lepton colliders are available, where any interested reader may find detailed reviews and technical challenges of not only advanced and novel e+ sources in future projects but also current conventional e+ sources.

In general, conventional e+ sources3–5 comprise an e+-production target and an e+ capture section subsequently located. Positrons are produced by impinging high-energy primary e beams with high intensity to a target of a high-Z material through an e+e pair-production process in an electromagnetic cascade shower.6 The total amount of produced positrons is principally dominated by two main parameters, for which one is the primary e beam power, the product of the e beam intensity and energy, and another is the target characteristics of material and thickness.1 The resulting transverse emittances of positrons secondarily generated from the target are very large due to the large momentum and angular spreads through an electromagnetic cascade shower process and multiple scattering in the target.

Some parts of the positrons are immediately captured in the e+ capture section, where they are focused in the transverse plane with strong axial magnetic fields, and they are captured in radio-frequency (rf) buckets of multiple accelerating structures (ACCs) in the longitudinal direction. Note that, in the e+ capture section, not only positrons but also secondarily generated electrons with approximately equivalent amounts of bunch charges simultaneously emerge from the target through this process. They are immediately simultaneously captured in the subsequent capture section. While the e bunch is stopped by a beam stopper after passing the capture section, the e+ bunch is separated from the e bunch and it is further accelerated by subsequent accelerating structures. The e+ intensity can be measured using a beam position monitor (BPM) (or beam intensity monitor) after the capture section.

An essential role of the e+ capture section is to increase the e+ capture efficiency as much as possible. The capture efficiency is generally simulated and optimized to increase it based on beam dynamics in multidimensional transverse and longitudinal parameter spaces, which are based on electromagnetic fields of accelerating structures and magnetic fields in the capture section. Moreover, the transverse parameters of the primary electrons, that is, transverse positions, injection angles, and impinging radii at the target, are also those in multidimensional parameter spaces. It is generally difficult to fully optimize the capture efficiency only by simulations. The optimization procedure should also be experimentally investigated to optimize it in multidimensional parameter spaces under realistic operating condition.

An objective function to be optimized is only the e+ intensity obtained after passing the e+ capture section because no instrumentation devices are installed in the e+ capture section. It is generally difficult to determine not the local optimum but the global optimum in terms of the e+ intensity with one objective function in multidimensional parameter spaces in conventional e+ sources. This is because it is difficult to separately measure the e+ and e bunches by a conventional technique in the capture section. For example, the time interval between the e and e+ bunches is very short to detect because the e and e+ bunches pass almost simultaneously in the capture section with a short time interval. The typical time interval between them is on the order of 100 ps. This is the reason why no beam parameters have ever been measured at the conventional e+ capture section.

It is challenging to simultaneously separately measure the e+ and e bunch characteristics to directly verify complicated beam dynamics in the capture section and to optimize the e+ intensity under the realistic operation condition. This is the main reason why the WBMs and their detection system were developed and installed at the e+ source of the SuperKEKB B-factory.

In a series of previous articles,7,8 it was reported that the secondarily generated e and e+ bunches in the e+ capture section were identified during their dynamical capture process as functions of the capture phase at locations of the WBMs under a two-bunch acceleration scheme. In this paper, it is subsequently reported in detail on the direct measurement results, which show the longitudinal and transverse bunch characteristics and their correlations. Based on the direct measurement results, the time intervals between the e and e+ bunches, the bunch lengths, transverse bunch positions, and bunch charges during their dynamical capture process are measured as functions of the capture phase.

The detailed design of the SuperKEKB B-factory complex has been already described elsewhere.9,10 The SuperKEKB B-factory (SKEKB) is a next-generation B-factory that is currently in operation at KEK after the KEKB B-factory11,12 (KEKB) was discontinued in 2010. SKEKB is an e+e collider with asymmetric energies; it comprises 4 GeV e+ (LER) and 7 GeV e (HER) rings in which the designed stored beam currents are 3.6 and 2.6 A, respectively. The target luminosity (8 × 1035 cm−2s−1) of SKEKB, that is, the rate of e and e+ collisions, is 40 times the peak luminosity of KEKB. To improve the collision rate, the development of a high-intensity and stable e+ source is one of the key elements in SKEKB.

The detailed design of the SKEKB injector linac has been already described elsewhere.13 The SKEKB injector linac is an ee+ linear accelerator for SKEKB; the KEKB injector linac14 was upgraded for the above-mentioned purpose. The requirement for the injector linac is full energy injection into the SKEKB rings with the e and e+ bunch charges of 5 and 4 nC, respectively. The injector linac should deliver low-emittance and high-current e and e+ single-bunched beams to the SKEKB rings. The high-intensity e+ beams are generated at the e+ source, and they are to be damped to the level required for the low-emittance beam through a damping ring.15 

The SKEKB e+ source is one of the conventional e+ sources and its schematic is shown in Fig. 1.

FIG. 1.

Schematic of the SKEKB e+ source; QFQD: quadrupole focusing (QF) and defocusing (QD) magnetic systems.

FIG. 1.

Schematic of the SKEKB e+ source; QFQD: quadrupole focusing (QF) and defocusing (QD) magnetic systems.

Close modal

Other designs have been already described in detail elsewhere.8,16 Here, only an additional explanation is given. Two conventional BPMs (SP15-15 and SP16-15) and two WBMs (SP15-25 and SP16-25) were newly installed along with three horizontal and one vertical steering magnets (STX and STY, respectively, dipole magnets for correcting a beam orbit in the transverse direction) in the capture section during the summer shutdown in 2020. These steering magnets are required to correct not only the transverse orbits of the e+ bunch due to the off-axis bombardment to the target but also any misalignments of the magnet system generating axial magnetic fields.

SP15-15 (SP15-25) is located 2.7 m (5.3 m) behind the target, and SP16-15 (SP16-25) is located 7.9 m (10.5 m) behind it. The conventional BPMs are used to measure the transverse positions and intensity of the injection e bunch with conventional detection electronics. On the other hand, the WBMs with a bandwidth of ∼10 GHz are used to simultaneously measure the transverse and longitudinal characteristics of both the e and e+ bunches secondarily generated at the target.

The detailed design of the WBMs was reported elsewhere.7 The signal detection system has already been reported in detail elsewhere.17 

The signal waveforms should be measured under appropriate conditions with corrections on any frequency-dependent amplitude losses and phase distortions of all the rf components, coaxial cables, signal combiners, and pickups. These can be corrected in the frequency domain in the oscilloscope by applying a standard fast-Fourier transformation (FFT) based on the frequency-dependent amplitude and phase data of any rf components in transmission, the so-called S21 parameter.18 The amplitude losses and phase distortions of all the coaxial cables and signal combiners were measured over the frequency region up to 13 GHz with a vector network analyzer (VNA) in advance.

Figure 2 shows the measurement results on the S21 parameters, (a) amplitude and (b) phase, for typical coaxial cables and the three different coaxial cables connected in series.

FIG. 2.

Measurement results on the S21 parameters, (a) amplitude and (b) phase, for typical coaxial cables and their connected cable in series.

FIG. 2.

Measurement results on the S21 parameters, (a) amplitude and (b) phase, for typical coaxial cables and their connected cable in series.

Close modal

The frequency-dependent amplitude loss of the coaxial cable is typically ∼−30 dB in total at a frequency of 10 GHz. Slight phase distortion can be found at frequencies higher than 10 GHz. Note that the amplitude loss of the 2 m-long semirigid PEEK (Poly Ether Ether Ketone) coaxial cable is dominant in the amplitude loss of the connected coaxial cable due to a large frequency-dependent amplitude loss caused by the use of PEEK; however, it is of great advantage in a hard radiation environment. These amplitude losses and phase distortions can be corrected by applying an inverse FFT using a software-based Bessel filter with fourth-order roll-off at a cutoff frequency of 9.1 GHz (see Ref. 18 for details) in this real-time oscilloscope. Therefore, any signal waveforms can be corrected in the frequency domain and displayed pulse-by-pulse in the time domain.

Note that four pickups of the WBM should also be corrected in the frequency domain. The signal transmission characteristics and detailed calibration procedure were investigated in the frequency region of up to 13 GHz based on a coupled-mode analysis using an equivalent circuit model with electromagnetically coupled transmission lines.19 The frequency characteristics of all the pickups were independently measured based on an electromagnetic induction method.

The electromagnetic induction method is briefly described here. An rf signal is sent to one of the four pickups and S21 parameters are obtained as a function of frequency by measuring the signals transmitted to other pickups using a VNA. In the signal transmission characteristics, the electromagnetic couplings between the pickups for fundamental and higher order rf waves play an important role depending on the spatial configuration, geometrical structure, and high-frequency signal loss of the pickups for a WBM with a cylindrical structure in the frequency region. Based on the electromagnetic induction method, the relative gain differences for all the pickups were measured in the calibration procedure. They were corrected to be 6% at maximum over the frequency region.

The signal waveform analysis procedure has been already described in detail elsewhere.8 It is briefly described here. The originally detected signal shows a differential waveform that has been already corrected in the frequency domain. The integrated waveform can be obtained by integrating the waveform data of the differential signal in the horizontal time axis. The e (e+) bunch can be identified by detecting the corresponding signal with minus (plus) polarity. The bunch characteristics are subsequently analyzed based on the results of the waveform analyses.

First, the time interval Δt between the e and e+ bunches can be obtained by measuring their peak positions in the time domain for the corresponding integrated waveforms. It is defined by the average value obtained from the four pickups to reduce any systematic errors between them as much as possible.

Second, the bunch length is defined by analyzing the pulse width in the integrated waveform. After finding the peak positions of the pulsed signal for both the e and e+ bunches, the time region of each pulsed signal is defined by identifying two first zero-cross points on both sides away from each peak position. The bunch length is defined by analyzing the root-mean-square (rms) pulse width using data points in the time region of the pulsed signal. It is also defined by the average value obtained from the four pickups to reduce any systematic errors between them as much as possible. For example, for the integrated waveform obtained at the capture phase Φ15 = 0°, the e and e+ bunch lengths (lb) are 36 and 37 ps in rms, respectively. The time resolution is 1.56 ps with the use of an interpolation function integrated into the oscilloscope, whereas the sampling speed is 40 GSa/s. Thus, the analysis of the bunch length with high precision is expected since there are sufficient data points on the order of more than ten for the rms width. However, note that there is a systematic error of 1.5 ps caused by the limitation of the frequency bandwidth and significant wakefields. They are discussed in detail elsewhere.8,20

Third, the bunch charge (or intensity) can be analyzed by calculating the pulsed area defined in the time region of the pulsed signal. It may be proportional to the pulsed area; however, bunch charges in the unit of nC should be calibrated. The detailed calibration procedure for the bunch charges was reported elsewhere.7 It is briefly described here. The calibration for the bunch charges is first carried out by using the charges measured using a BPM (SP16-5), which has been already calibrated for single-bunched e and e+ injection bunches. Here, an e injection bunch with charges of 2 nC rather than the use of the secondarily generated e+ bunch was applied for the calibration procedure because the obtained signal was one simple bipolar signal, which may effectively reduce the effect of the transient response compared with two successive bipolar signals. However, owing to the bandwidth limitation for the pulsed area analysis, it was found that the first calibration procedure was insufficient. Thus, the second calibration procedure was applied, which was based on corrections to the first calibration procedure by using a bandwidth of up to 20 GHz. After the second calibration procedure, the calibration coefficient was obtained, which transformed the pulsed area of the bunch into bunch charges. Note that there are also other systematic errors due to wakefields, which were estimated to be ∼30% at maximum (see Ref. 20 for details).

Finally, the transverse positions of the bunch can be analyzed by using the pulsed areas obtained from the four pickups. They can be derived by a conventional beam position analysis procedure.21 Thus, in terms of both the e and e+ bunch characteristics, the time interval, bunch lengths, transverse bunch positions, and bunch charges can be simultaneously separately obtained.

Note that there are still some deficiencies in the bunch characteristics, that is, bunch energies, energy spreads, and transverse sizes, and therefore, more strictly speaking, any wakefield effects from accelerating structures and any misalignments in the longitudinal and transverse directions for the accelerating structures and solenoid coils should also be investigated. It is generally difficult to measure these bunch characteristics without disrupting the operation conditions. Although the operation conditions in the measurements are disrupted, by changing any parameters in the operation condition, they may be obtained by directly measuring the bunch intensity at SP16-5 depending on the magnetic field strength of the chicane (or the transverse positions of the beam stopper under the condition that the field strength of the chicane is kept constant). These bunch characteristics are also important parameters in multidimensional parameter spaces.

Figure 3 shows the variations in the e and e+ first bunch characteristics as functions of the capture phase Φ15 with a step phase of 10°, for which the phase Φ16 was concurrently changed by the same step phase. Figure 3(a) shows the variations obtained at SP15-25, and Fig. 3(b) shows the variations obtained at SP16-25.

FIG. 3.

Variations in the e and e+ bunch characteristics of the first bunch as functions of the capture phase Φ15 with a step phase of 10°, for which the phase Φ16 was concurrently changed by the same step phase. Characteristics of the (a) e and (b) e+ bunches at SP15-25 and those of the (c) e and (d) e+ bunches at SP16-25. Note that e@ee+ (e@e+e) indicates the e bunch in the configuration of the front (rear) e bunch and rear (front) e+ bunch in the accelerating (decelerating) region, and e+@e+e (e+@ee+) similarly indicates the e+ bunch in the configuration of the front (rear) e+ bunch and rear (front) e bunch in their role replaced between the e and e+ bunches.

FIG. 3.

Variations in the e and e+ bunch characteristics of the first bunch as functions of the capture phase Φ15 with a step phase of 10°, for which the phase Φ16 was concurrently changed by the same step phase. Characteristics of the (a) e and (b) e+ bunches at SP15-25 and those of the (c) e and (d) e+ bunches at SP16-25. Note that e@ee+ (e@e+e) indicates the e bunch in the configuration of the front (rear) e bunch and rear (front) e+ bunch in the accelerating (decelerating) region, and e+@e+e (e+@ee+) similarly indicates the e+ bunch in the configuration of the front (rear) e+ bunch and rear (front) e bunch in their role replaced between the e and e+ bunches.

Close modal

Each data point was repeatedly measured 100 times for averaging with an error of one standard deviation including any systematic errors. Note that different colors in the bunch characteristics were used for the e and e+ bunches. The different colors in each bunch indicate the bunch characteristics in the accelerating (or decelerating) phase region. Three specific data points are also shown by “oper. point” under the nominal operation condition and by “Qmax point” at the maximum charge in the accelerating and decelerating phase regions.

First, it can be seen that there are two intersections in the time interval variations at Δt = 0. One is at Φ15 ≃ 50° and the other is at Φ15 ≃ 250°. The results show that the line-order switch for the e and e+ bunches due to their dynamical phase-slip process in the axial direction was observed as functions of the capture phase (see elsewhere8 for details). The e+ bunch precedes the e bunch in the phase region of Φ15 ≃ 50°–250°, which corresponds to Δt < 0. In other words, it means that the e+ (e) bunch is in the accelerating (decelerating) phase region for AC15. On the other hand, the e bunch precedes the e+ bunch in the phase regions of Φ15 ≃ 0°–50° and Φ15 ≃ 250°–360°, which correspond to Δt > 0. This result means that the e (e+) bunch is in the accelerating (decelerating) region for AC15. Thus, it can be understood that the e+ (e) bunch is in the decelerating (accelerating) region under the nominal operation condition (see elsewhere8 for details).

Second, the length variations for the e and e+ bunches are shown as functions of the capture phase. The bunch lengths are in the range of lb ≃ 14 ps to lb ≃ 50 ps in rms. It can be found that they show quite symmetric behaviors between the e and e+ bunches in comparison with those in the same corresponding accelerating (or decelerating) phase region. It is interesting to note the discontinuities at the two intersections in the time interval because of different longitudinal dynamics at which the acceleration and deceleration for both the e and e+ bunches are switched.

Third, the variations in the transverse positions for the e and e+ bunches are shown as functions of the capture phase. Since high-intensity primary electrons impinge the target at 3.5 mm off-axis in the horizontal direction from the target center, it can be seen that with the use of steering magnets, the detected horizontal (x) position is ∼−2 mm and the vertical (y) position is ∼0 mm at SP15-25, whereas the x positions approach ∼0 mm at SP16-25 and the y positions show almost no difference. Note that there are relatively large position displacements in both the x and y directions at the capture phases close to the two intersections because of different longitudinal dynamics.

Finally, the charge variations for the e and e+ bunches are shown as functions of the capture phase. It is interesting to note that there are two peak points in the region of the capture phases for both the e and e+ bunches. One is the peak point at Φ15 ≃ 100° in the accelerating (decelerating) phase region for the e+ (e) bunch, and the other is that at Φ15 ≃ 280° (Φ15 ≃ 290°) in the accelerating (decelerating) phase region for the e (e+) bunch. It is also interesting to note that the maximum charges for the e bunch at SP15-25 in the accelerating phase region are ∼15% greater than those for the e+ bunch at SP15-25 in the accelerating phase region. This is caused by the Compton effect,22  e+ annihilation process, and δ-rays generation process dominating in the secondary e generation through electromagnetic interaction in the target in comparison with the secondary e+ generation. It can be found that both the behaviors in the bunch charge variations are also quite symmetric. Similar variations in the e and e+ second bunch characteristics were obtained; however, the results are omitted here.

Figure 4 shows the variations in the position displacements in the transverse plane for the e and e+ bunches at SP15-25 and SP16-25 including all the data points. Figure 4(a) shows the variations for the accelerated and decelerated e bunches, and Fig. 4(b) shows those for the accelerated and decelerated e+ bunches.

FIG. 4.

Variations in the position displacements in the transverse plane for the accelerated and decelerated (a) e bunches and (b) e+ bunches at SP15-25 and SP16-25 including all the data points.

FIG. 4.

Variations in the position displacements in the transverse plane for the accelerated and decelerated (a) e bunches and (b) e+ bunches at SP15-25 and SP16-25 including all the data points.

Close modal

It can be found that there are almost no characteristic differences in the transverse positions depending on the capture phases, even at the capture phase under the nominal operating condition and at the characteristic capture phases giving the maximum charge. It is interesting to note that the cluster for each e and e+ bunch rotates in the transverse plane owing to the cyclotron motion in the longitudinal direction between SP15-25 and SP16-25.

The transverse positions (x, y) in the center of gravity for each cluster in the accelerated and decelerated e bunches [corresponding to e@ee+ and e@e+e, respectively, in Fig. 4(a)] are (−2.3 ± 0.5 mm, 0.3 ± 1.4 mm) and (−1.9 ± 0.3 mm, 0.5 ± 0.5 mm) at SP15-25, and (0.5 ± 0.7 mm, −1.5 ± 0.8 mm) and (0.8 ± 0.6 mm, −1.0 ± 0.9 mm) at SP16-25, respectively. Those for the accelerated and decelerated e+ bunches [corresponding to e+@e+e and e+@ee+, respectively, in Fig. 4(b)] are (−1.6 ± 0.4 mm, 0.6 ± 0.6 mm) and (−2.3 ± 1.5 mm, −0.3 ± 0.7 mm) at SP15-25, and (1.1 ± 1.0 mm, 0.3 ± 1.0 mm) and (−0.2 ± 1.8 mm, 0.4 ± 0.8 mm) at SP16-25, respectively. The measurement errors for each cluster are given in rms. It is interesting to note that the rotational behaviors are similar among the accelerated and decelerated e (as well as e+) bunches. However, those for the e bunches are slightly different from those for the e+ bunches. This is because the steering magnetic force may oppositely act in the motions of e and e+ bunches.

The time intervals and charges in the accelerated and decelerated e and e+ bunches were simultaneously separately measured at SP15-25 and SP16-25 including all the data points. Figure 5 shows the variations in the correlations in terms of the time intervals and bunch charges for the accelerated and decelerated e (or e+) bunches and their charges at SP16-25 to those at SP15-25 including all the data points. Note that the time intervals analyzed for the e and e+ bunches are the same according to their definition. Figure 5(a) shows the variations in the correlations for the accelerated and decelerated e bunches, and Fig. 5(b) shows those for the accelerated and decelerated e+ bunches.

FIG. 5.

Variations in the correlations between the time intervals and charges in the accelerated and decelerated (a) e bunches and (b) e+ bunches at SP15-25 and SP16-25 including all the data points. The solid lines are only to guide the eye.

FIG. 5.

Variations in the correlations between the time intervals and charges in the accelerated and decelerated (a) e bunches and (b) e+ bunches at SP15-25 and SP16-25 including all the data points. The solid lines are only to guide the eye.

Close modal

It can be found that all the data points clearly form a straight line tilted by 45° with respect to the horizontal axis in the accelerated and decelerated e and e+ bunches. The results again show that the phase-slip process occurs during the passage in AC15 and it is fixed at AC16. They also show that the time intervals giving the maximum charge are obtained at approximately the largest time intervals, in other words, at which the phase slip is caused to a maximum degree in AC15. The time intervals at the maximum charge are obtained at Δt = −268 ± 11 ps and Δt = 264 ± 9 ps on average for the decelerated and accelerated e bunches, respectively. On the other hand, the time intervals are obtained at Δt = −268 ± 11 ps and Δt = 253 ± 7 ps on average for the accelerated and decelerated e+ bunches, respectively. It can be seen that their behaviors for the e and e+ bunches are quite symmetric, whereas the variations in the e bunch charges at SP15-25 and SP16-25 depending on the time interval are slightly different from those in the e+ bunch charges. Note that there are two data points giving the maximum charge in the correlations for the e and e+ bunches. One is the maximum charge for the accelerated bunches, and the other is that for the decelerated bunches. The charges at maximum for the accelerated and decelerated e (e+) bunches are 9.8 ± 0.4 nC (8.3 ± 0.3 nC) and 7.8 ± 0.3 nC (7.5 ± 0.3 nC) at SP15-25, and those are 10.0 ± 0.4 nC (8.2 ± 0.4 nC) and 7.3 ± 0.3 nC (6.8 ± 0.5 nC) at SP16-25, respectively. The ratios of the maximum charges for the decelerated e (e+) bunch to that for the accelerated e (e+) bunch are ∼80% (∼90%) and ∼73% (∼83%) at SP15-25 and SP16-25, respectively. The results show that the ratios for the e+ bunches are ∼10% greater than those for the e bunches at both the locations of SP15-25 and SP16-25, whereas the transmission in the bunch charge from SP15-25 to SP16-25 is 100% (99%) for the accelerated e (e+) bunches and it is 94% (91%) for the decelerated e (e+) bunches. Note that the operation point under the nominal operation condition does not agree with any points giving the maximum charge. It is interesting to note that the maximum charge is obtained at the accelerating phase region rather than the decelerating phase region in both the e and e+ bunches.

Figure 6 shows the variations in the correlations in terms of the bunch lengths and charges for the e and e+ bunches at SP15-25 and SP16-25 including all the data points. Figure 6(a) shows the variations for the accelerated and decelerated e bunches, and Fig. 6(b) shows the variations for the accelerated and decelerated e+ bunches.

FIG. 6.

Variations in the correlations in the bunch lengths and charges for the accelerated and decelerated (a) e bunches and (b) e+ bunches at SP15-25 and SP16-25 including all the data points. The solid lines are only to guide the eye.

FIG. 6.

Variations in the correlations in the bunch lengths and charges for the accelerated and decelerated (a) e bunches and (b) e+ bunches at SP15-25 and SP16-25 including all the data points. The solid lines are only to guide the eye.

Close modal

It is found that the data points in the correlations are on a polynomial curved line rather than on a straight line tilted by 45° with respect to the horizontal axis in both the accelerated e and e+ bunches. The result shows that although the phase-slip process halts during the passage in AC15, the bunch lengthening (or shortening) is generated owing to particle displacement in the bunch in the longitudinal direction in accordance with the longitudinal dynamics depending on the capture phases. The correlation for the accelerated e bunches shows that there are two intersection points at the bunch lengths of lb ≃ 27 ps and lb ≃ 48 ps. The bunch length at SP16-25 is greater than that at SP15-25 in the region of less than 27 ps. The relative bunch lengthening (shortening) is defined by the ratio [1 (<1)] of the bunch length at SP16-25 to that at SP15-25. Note that the bunch lengthening is generated at SP16-25 in this region. The bunch shortening is generated at SP16-25 in the region between 27 and 48 ps. The bunch lengths giving the maximum charge are obtained at approximately the largest bunch lengths, which are lb ≃ 48 ± 2 ps and lb ≃ 47 ± 2 ps at SP15-25 and SP16-25, respectively. On the other hand, the correlation for the decelerated e bunch shows that there are no intersection points and the data points are located within the narrow regions in the bunch length, in which the bunch shortening is generated. The bunch lengths giving the maximum charge are similarly obtained at approximately the largest bunch lengths, which are lb ≃ 40 ± 2 ps and lb ≃ 36 ± 2 ps at SP15-25 and SP16-25, respectively.

It can be seen that in terms of the e+ bunch, the behavior of variations in the correlation is similar to that of the e bunch. The correlation in the accelerated e+ bunch shows that there are three intersection points at the bunch lengths of lb ≃ 18 ps, lb ≃ 29 ps, and lb ≃ 48 ps. The bunch shortening is generated at SP16-25 in the region of less than 18 ps. The bunch lengthening is generated at SP16-25 in the region between 18 and 29 ps. The bunch shortening is again generated at SP16-25 in the region of greater than 29 ps. The bunch lengths giving the maximum charge are similarly obtained at the maximum bunch lengths of lb ≃ 48 ± 2 ps and lb ≃ 46 ± 2 ps at SP15-25 and SP16-25, respectively. On the other hand, the correlation in the decelerated e+ bunch shows that there are no intersection points and the data points are similarly located within the narrow regions in the bunch length, where the bunch shortening is generated. The bunch lengths giving the maximum charge are similarly obtained at approximately the largest bunch lengths, which are lb ≃ 35 ± 2 ps and lb ≃ 31 ± 2 ps at SP15-25 and SP16-25, respectively. The results show that quite symmetric behaviors for the e and e+ bunches are observed, whereas the lengths of the e bunch giving the maximum charge are greater than those for the e+ bunch. This may be because the charges for the e bunch are greater than those for the e+ bunch.

It can be found that both the decelerated e and e+ bunches are located within the narrow regions in the bunch length. The results show that the decelerated bunches may not be of advantage in comparison with the accelerated ones from the viewpoints of charge excess because any slight fluctuations in bunch length may cause serious degradation of bunch charges.

The bunch charges simultaneously obtained for the e and e+ bunches at SP15-25 and SP16-25 in the capture section, and for the e+ bunch at SP16-5 immediately after the chicane, are analyzed here and the variations in those for the e and e+ bunches depending on the capture phases are summarized.

Figure 7 shows the variations in the charges for the e and e+ bunches at SP15-25 and SP16-25, and for the e+ bunch at three locations, SP15-25, SP16-25, and SP16-5 as functions of the capture phase. Figure 7(a) shows those for the e and e+ bunches at SP15-25, Fig. 7(b) shows those at SP16-25, and Fig. 7(c) shows those for the e+ bunch at SP15-25, SP16-25, and SP16-5.

FIG. 7.

Variations in the bunch charges for the e and e+ bunches at (a) SP15-25 and (b) SP16-25, and (c) for the e+ bunch at three locations, SP15-25, SP16-25, and SP16-5 as functions of the capture phase. The solid lines are only to guide the eye.

FIG. 7.

Variations in the bunch charges for the e and e+ bunches at (a) SP15-25 and (b) SP16-25, and (c) for the e+ bunch at three locations, SP15-25, SP16-25, and SP16-5 as functions of the capture phase. The solid lines are only to guide the eye.

Close modal

The results show that quite symmetric behaviors in terms of the variations in the charges for the e and e+ bunches are observed except for the charge excess for the e bunch, which has been already described in Sec. V A. It can be seen that there are two capture phases in the accelerated and decelerated regions giving the maximum charge at which the capture phases for the e bunch agree with those for the e+ bunch with high accuracy. It is important to point out that the charge excess at the capture phase in the accelerated region is 20% (10%) relative to that in the decelerated region for the e (e+) bunch at SP15-25 [see Fig. 7(a)]. On the other hand, the charge excess is 27% (17%) for the e (e+) bunch at SP16-25 [see Fig. 7(b)]. The results show that the accelerated bunch may be of great advantage to the decelerated bunch from the viewpoints of the bunch charge excess in the capture section.

Here, let us pay attention to the charge variations in the e+ bunch as functions of the capture phase at three locations, SP15-25, SP16-25, and SP16-5, as shown in Fig. 7(c). The e+ bunch charges should be fixed to their maximum at SP16-5 by varying any parameters in multidimensional parameter spaces in the nominal operation. The result is shown by the variations indicated by the brown curve in Fig. 7(c). The e+ bunch charges are 4.5 ± 0.2 nC, 8.3 ± 0.3 nC, and 7.5 ± 0.3 nC at SP15-25, which correspond to the maximum charge under the nominal operation condition, the maximum charge in the accelerated phase region, and the maximum charge in the decelerated phase region, respectively. They correspond to 3.7 ± 0.2 nC, 8.2 ± 0.4 nC, and 6.8 ± 0.3 nC at SP16-25. They also correspond to 3.8 ± 0.1 nC, 4.0 ± 0.1 nC, and 4.1 ± 0.2 nC at SP16-5. It is found that the charge losses in the e+ bunch at SP16-5 are larger than those at SP15-25 and SP16-25, whereas there are almost no charge losses in the capture section. It is also found that the bunch charges under the nominal operation condition are not maximum and this operation point is far from the capture phase giving the maximum charge in the accelerated (or decelerated) phase region. It is also far from those at SP15-25 and SP16-25.

The results show that the charge excess in the e+ bunch at the capture phase giving the maximum charge in the accelerated and decelerated phase regions relative to those under the nominal operation condition is only 5% at SP16-5. On the other hand, the charge excesses are 122% and 84% at SP16-25 at the capture phase giving the maximum charge in the accelerated and decelerated phase regions, respectively. Note that there is a significant difference in the charge excess for both the e and e+ bunches at SP15-25 and SP16-25 in the capture section, whereas there is only a minute difference at SP16-5. The capture phases giving the maximum charge in the accelerated and decelerated phase regions at SP16-5 are 120° and 330°, which are shifted by 20° and 40° from those giving the maximum charge at SP16-25, respectively. This is the main reason why it is difficult to optimize the e+ bunch charges at maximum only by measuring those at SP16-5 without measuring the e and e+ bunch characteristics inside the capture section.

It is important to point out which capture phase is of advantage from the viewpoint of the charge excess at SP16-5. However, it is difficult to give any answers here because, in this experiment, there are other unknown bunch characteristics, namely, the energies, energy spreads, and transverse sizes for both the e and e+ bunches in the capture section. The optics matching condition at the location of the chicane should also be verified to enhance the transmission of the e+ bunch charges to downstream accelerator sections. To fully optimize the e+ bunch charges, more experimental data including other e and e+ bunch characteristics should be obtained along with detailed simulations not only in the e+ capture section but also including downstream accelerator sections based on the optics for the e+ bunch.

Direct simultaneous measurements of the secondarily generated e and e+ bunch characteristics were successfully performed with the new WBMs and their detection system at the e+ capture section of the SuperKEKB B-factory. For the first time, the longitudinal and transverse bunch characteristics, the time intervals between the e and e+ first and second bunches, their bunch lengths, their transverse positions, and their bunch charges were simultaneously separately obtained for each bunch as functions of the capture phase to investigate their dynamical capture process under the two-bunch acceleration scheme. The results show that quite symmetric behaviors between the e and e+ bunch characteristics were observed. Such wideband detection techniques can be applied to not only conventional e+ sources but also advanced e+ sources in future accelerator projects. The obtained results may also improve simulations in any e+ capture sections, and thus, the e+ intensity can be systematically fully optimized by applying this technique along with detailed simulations in multidimensional parameter spaces toward high-intensity e+ sources.

The author would like to thank the operators of the injector linac for their help during this experiment. The author would also like to thank Dr. M. A. Rehman of IHEP for his significant contribution to this experiment. This study was fully supported by Grants-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan.

The authors have no conflicts to disclose.

Tsuyoshi Suwada: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Funding acquisition (lead); Investigation (lead); Methodology (lead); Project administration (lead); Resources (lead); Supervision (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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